Problem: Simplify the following expression: $ q = \dfrac{10k + 5}{-8} - \dfrac{-9}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{10k + 5}{-8} \times \dfrac{4}{4} = \dfrac{40k + 20}{-32} $ Multiply the second expression by $\dfrac{-8}{-8}$ $ \dfrac{-9}{4} \times \dfrac{-8}{-8} = \dfrac{72}{-32} $ Therefore $ q = \dfrac{40k + 20}{-32} - \dfrac{72}{-32} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{40k + 20 - 72 }{-32} $ Distribute the negative sign: $q = \dfrac{40k + 20 - 72}{-32}$ $q = \dfrac{40k - 52}{-32}$ Simplify the expression by dividing the numerator and denominator by -4: $q = \dfrac{-10k + 13}{8}$